Background

This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. biomass relationships. We use the mass balance biomass growth method for the plot biomass growth (\(G\)) calculation (briefly, plot biomass growth is a function of the change in plot biomass plus any losses due to mortality or harvest over time: \(G_{MB} = (\Delta B + M_t + C_t) / REMPER\), where \(\Delta B\) is change in plot biomass over a census interval ( \(\Delta B = B_{t + \Delta g} - B_t\) ), and \(M_t\) and \(C_t\) is the biomass of trees that died or were harvested, respectively, between two plot measurements. note: \(REMPER\) is time between two plot measurement intervals (FIA re-measurement period). For additional details see supplementary methods. Models are fitted separately by US ecoprovince.

Hypothetically, the entire functional form of the following Michaelis-Menten non-linear model is considered: \(G = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(B_{t1}\) is the plot biomass at the first of two FIA plot tree censuses, and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(tau\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Data have increasing variance in \(G\) with increasing \(B\), thus, weighted nls is the best approach. We explored a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {mean B_{t1}}\) in equal-sample sized plot biomass bins (n=20 where possible, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.

Model selection is used to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine if including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest) is warranted:

model 1: simple tau model \(G = (1 + (yr-1990)* \tau/100) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

model 2: tau-alpha model \(G = (1 + (yr-1990)* \tau/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

Then, a second model selection is done using best-fitting model from part 1 and then considering additional \(p\) and \(s\) parameters (individually, and then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p)A \cdot B_{t1}} {k+B_{t1}} \right)\)

sub model b: s form \(\left( \frac {A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)

sub model c: p and s together \(pA + \left( \frac {(1-p)A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)

NOTE:

This document contains all \(G\) observations that meet our plot-based filtering criteria:

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile thresholding approach. We also calculated plot \(G_{TI}\) using as summed tree incremental growth for all trees > 12.5 cm (5 inches) (see supplementary methods). We use the difference between the two methods, which we define \(diff_G\) as the difference between the two methods \(G_{MB} - G_{TI}\) to identify erroneous or outlier growth calculations. We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):

  • case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)

  • case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)

  • case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)

  • case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)

These data set cleaning criteria resulted in the exclusion of 1760 observations.

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6528     6446.0                                
## 2   6527     6168.5  1 277.57   293.7 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 26044.32
## 2     2 25758.85
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.19616    0.17071   1.149    0.251    
## alpha -0.63021    0.03446 -18.286  < 2e-16 ***
## A      3.54580    0.12577  28.192  < 2e-16 ***
## k      6.08478    0.97267   6.256 4.21e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9721 on 6527 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 1.079e-06
##   (353 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   6527     6168.5                            
## 2   6526     6165.4  1 3.0319  3.2092 0.07327 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 25758.85
## 2    2a 25757.64
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.18836    0.17032   1.106    0.269    
## alpha  0.62749    0.03454  18.168   <2e-16 ***
## A      3.79577    0.24275  15.636   <2e-16 ***
## k     70.36150   59.12289   1.190    0.234    
## p      0.69559    0.04706  14.781   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.972 on 6526 degrees of freedom
## 
## Number of iterations to convergence: 14 
## Achieved convergence tolerance: 8.494e-06
##   (353 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: Removed 26 rows containing missing values (`geom_point()`).
## Warning: Removed 1038 rows containing missing values (`geom_line()`).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  18496      19634                                
## 2  18495      18485  1   1149  1149.6 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 69051.88
## 2     2 67938.32
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.38955    0.17879   7.772 8.13e-15 ***
## alpha -0.81312    0.02198 -36.993  < 2e-16 ***
## A      2.49608    0.07001  35.655  < 2e-16 ***
## k     11.16662    0.50650  22.046  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9997 on 18495 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.175e-06
##   (4186 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  18495      18485                                
## 2  18494      18441  1 44.079 44.2067 3.037e-11 ***
## 3  18494      18438  0  0.000                      
## 4  18493      18438  1  0.023  0.0235    0.8781    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 67938.32
## 2    2a 67896.16
## 3    2b 67892.98
## 4    2c 67894.96
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.35712    0.17684   7.674 1.75e-14 ***
## alpha  0.81019    0.02203  36.773  < 2e-16 ***
## A      3.13642    0.20040  15.651  < 2e-16 ***
## k     19.51596    4.10501   4.754 2.01e-06 ***
## s      0.58373    0.05366  10.879  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9985 on 18494 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 8.771e-06
##   (4186 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

predict and plot

## Warning: Removed 1889 rows containing missing values (`geom_point()`).
## Warning: Removed 1031 rows containing missing values (`geom_line()`).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6938     9391.8                                
## 2   6937     8982.7  1 409.15  315.97 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 30727.86
## 2     2 30420.69
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.67555    0.13143  -5.140 2.82e-07 ***
## alpha -0.74229    0.03917 -18.950  < 2e-16 ***
## A      5.35702    0.19707  27.183  < 2e-16 ***
## k     23.62690    2.78246   8.491  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.138 on 6937 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.47e-06
##   (366 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_221,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     2 30420.69
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.67555    0.13143  -5.140 2.82e-07 ***
## alpha -0.74229    0.03917 -18.950  < 2e-16 ***
## A      5.35702    0.19707  27.183  < 2e-16 ***
## k     23.62690    2.78246   8.491  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.138 on 6937 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.47e-06
##   (366 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## Warning: Removed 31 rows containing missing values (`geom_point()`).
## Warning: Removed 1036 rows containing missing values (`geom_line()`).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4746     5808.2                                
## 2   4745     5533.6  1 274.52   235.4 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19696.25
## 2     2 19468.31
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.16997    0.23340   0.728    0.467    
## alpha -0.76634    0.04579 -16.737   <2e-16 ***
## A      4.26363    0.20256  21.049   <2e-16 ***
## k     21.25535    1.77327  11.987   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.08 on 4745 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.14e-06
##   (1097 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4745     5533.6                                
## 2   4744     5444.3  1 89.341  77.849 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 19468.31
## 2    2a 19393.01
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.03824    0.22050   0.173   0.8623    
## alpha   0.75920    0.04542  16.714  < 2e-16 ***
## A       8.42134    1.45931   5.771 8.39e-09 ***
## k     317.27298  110.77065   2.864   0.0042 ** 
## p       0.22857    0.03088   7.401 1.59e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.071 on 4744 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.202e-06
##   (1097 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## Warning: Removed 488 rows containing missing values (`geom_point()`).
## Warning: Removed 1053 rows containing missing values (`geom_line()`).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8496    10221.3                                
## 2   8495     9933.6  1 287.73  246.06 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 34871.18
## 2     2 34630.50
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.59402    0.12174  -4.879 1.08e-06 ***
## alpha -0.67655    0.04042 -16.738  < 2e-16 ***
## A      5.14680    0.18549  27.748  < 2e-16 ***
## k     42.04611    3.37270  12.467  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.081 on 8495 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.908e-06
##   (1507 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model     AIC
## 1     2 34630.5
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.59402    0.12174  -4.879 1.08e-06 ***
## alpha -0.67655    0.04042 -16.738  < 2e-16 ***
## A      5.14680    0.18549  27.748  < 2e-16 ***
## k     42.04611    3.37270  12.467  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.081 on 8495 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.908e-06
##   (1507 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## Warning: Removed 612 rows containing missing values (`geom_point()`).
## Warning: Removed 1127 rows containing missing values (`geom_line()`).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12213      25243                                
## 2  12212      22266  1 2977.6  1633.1 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 61285.28
## 2     2 59754.04
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.7192     0.1924   8.937  < 2e-16 ***
## alpha  -0.8762     0.0195 -44.929  < 2e-16 ***
## A       3.8181     0.1117  34.191  < 2e-16 ***
## k       2.5595     0.3934   6.506 8.03e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.35 on 12212 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.642e-06
##   (628 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_231,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1  12212      22266                          
## 2  12211      22265  1 0.89592  0.4914 0.4833
##   model      AIC
## 1     2 59754.04
## 2    2a       NA
## 3    2b 59755.55
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.7192     0.1924   8.937  < 2e-16 ***
## alpha  -0.8762     0.0195 -44.929  < 2e-16 ***
## A       3.8181     0.1117  34.191  < 2e-16 ***
## k       2.5595     0.3934   6.506 8.03e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.35 on 12212 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.642e-06
##   (628 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: fits
  • add s+p model: does not fit

predict and plot

## Warning: Removed 121 rows containing missing values (`geom_point()`).
## Warning: Removed 1017 rows containing missing values (`geom_line()`).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12486      31324                                
## 2  12485      27933  1 3390.8  1515.6 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 63593.26
## 2     2 62164.41
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.3894     0.2016    6.89 5.85e-12 ***
## alpha  -0.8713     0.0198  -44.01  < 2e-16 ***
## A       3.9059     0.1289   30.30  < 2e-16 ***
## k       6.3334     0.5191   12.20  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.496 on 12485 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.065e-06
##   (678 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12485      27933                                
## 2  12484      27900  1 33.550  15.012 0.0001074 ***
## 3  12484      27908  0  0.000                      
## 4  12483      27894  1 14.491   6.485 0.0108905 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 62164.41
## 2    2a 62151.40
## 3    2b 62155.33
## 4    2c 62150.84
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    1.37237    0.20054   6.843 8.10e-12 ***
## alpha  0.87172    0.01979  44.055  < 2e-16 ***
## A      3.89136    0.14849  26.207  < 2e-16 ***
## k     26.06148    4.92503   5.292 1.23e-07 ***
## s      1.60320    0.40302   3.978 6.99e-05 ***
## p      0.54938    0.06617   8.302  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.495 on 12483 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.389e-06
##   (678 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

predict and plot

## Warning: Removed 153 rows containing missing values (`geom_point()`).
## Warning: Removed 953 rows containing missing values (`geom_line()`).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1274     2866.7                                
## 2   1273     2700.1  1 166.61  78.548 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6409.271
## 2     2 6334.811
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.8095     0.6929   1.168  0.24289    
## alpha  -0.7606     0.0775  -9.814  < 2e-16 ***
## A       3.9836     0.5071   7.856 8.39e-15 ***
## k       3.7233     1.3736   2.711  0.00681 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.456 on 1273 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.333e-06
##   (67 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1   1273     2700.1                         
## 2   1272     2697.6  1 2.5536  1.2041 0.2727
##   model      AIC
## 1     2 6334.811
## 2    2a 6335.603
## 3    2b 6334.990
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.8095     0.6929   1.168  0.24289    
## alpha  -0.7606     0.0775  -9.814  < 2e-16 ***
## A       3.9836     0.5071   7.856 8.39e-15 ***
## k       3.7233     1.3736   2.711  0.00681 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.456 on 1273 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.333e-06
##   (67 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

predict and plot

## Warning: Removed 22 rows containing missing values (`geom_point()`).
## Warning: Removed 948 rows containing missing values (`geom_line()`).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1     76     136.79                            
## 2     75     125.36  1 11.426   6.836 0.01079 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 421.2541
## 2     2 416.3630
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau    -0.9701     1.7313  -0.560  0.57692   
## alpha  -0.9705     0.3345  -2.901  0.00488 **
## A       9.7517     4.4803   2.177  0.03266 * 
## k      20.9759    15.5170   1.352  0.18050   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.293 on 75 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.047e-06
##   (6 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_242,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model     AIC
## 1     2 416.363
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau    -0.9701     1.7313  -0.560  0.57692   
## alpha  -0.9705     0.3345  -2.901  0.00488 **
## A       9.7517     4.4803   2.177  0.03266 * 
## k      20.9759    15.5170   1.352  0.18050   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.293 on 75 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.047e-06
##   (6 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## Warning: Removed 2 rows containing missing values (`geom_point()`).
## Warning: Removed 725 rows containing missing values (`geom_line()`).

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1740     2174.3                                
## 2   1739     2160.3  1 14.052  11.312 0.0007869 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7121.686
## 2     2 7112.386
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.4136     0.4550   0.909 0.363521    
## alpha  -0.3868     0.1103  -3.506 0.000467 ***
## A       3.4066     0.3072  11.088  < 2e-16 ***
## k      19.8898     3.6894   5.391 7.96e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.115 on 1739 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.963e-06
##   (547 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_251,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     2 7112.386
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.4136     0.4550   0.909 0.363521    
## alpha  -0.3868     0.1103  -3.506 0.000467 ***
## A       3.4066     0.3072  11.088  < 2e-16 ***
## k      19.8898     3.6894   5.391 7.96e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.115 on 1739 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.963e-06
##   (547 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## Warning: Removed 249 rows containing missing values (`geom_point()`).
## Warning: Removed 1176 rows containing missing values (`geom_line()`).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    639     1515.9                                
## 2    638     1458.2  1 57.633  25.215 6.662e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2995.098
## 2     2 2972.213
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.4255     0.9432   0.451    0.652    
## alpha  -0.7802     0.1391  -5.609 3.03e-08 ***
## A       2.8095     0.5085   5.525 4.82e-08 ***
## k       1.8978     2.2196   0.855    0.393    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.512 on 638 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.496e-06
##   (72 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_255,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    638     1458.2                         
## 2    637     1457.0  1 1.1985   0.524 0.4694
##   model      AIC
## 1     2 2972.213
## 2    2a       NA
## 3    2b 2973.686
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.4255     0.9432   0.451    0.652    
## alpha  -0.7802     0.1391  -5.609 3.03e-08 ***
## A       2.8095     0.5085   5.525 4.82e-08 ***
## k       1.8978     2.2196   0.855    0.393    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.512 on 638 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.496e-06
##   (72 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91522, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.246, p-value = 2.177e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 22 rows containing missing values (`geom_point()`).
## Warning: Removed 1235 rows containing missing values (`geom_line()`).

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • note: model fit, but fit was funky due to data being sparse

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    203     98.779                              
## 2    202     94.169  1 4.6095  9.8877 0.001915 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 474.7048
## 2     2 466.8603
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.3054     0.8972  -1.455 0.147197    
## alpha  -0.8771     0.2465  -3.559 0.000464 ***
## A       5.1018     1.7192   2.968 0.003365 ** 
## k     144.9621    49.7005   2.917 0.003938 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6828 on 202 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.054e-06
##   (12 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    202     94.169                          
## 2    201     93.989  1 0.18070  0.3864 0.5349
## 3    201     94.111  0 0.00000               
## 4    200     93.424  1 0.68623  1.4691 0.2269
##   model      AIC
## 1     2 466.8603
## 2    2a 468.4646
## 3    2b 468.7317
## 4    2c 469.2240
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.3054     0.8972  -1.455 0.147197    
## alpha  -0.8771     0.2465  -3.559 0.000464 ***
## A       5.1018     1.7192   2.968 0.003365 ** 
## k     144.9621    49.7005   2.917 0.003938 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6828 on 202 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.054e-06
##   (12 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

predict and plot

## Warning: Removed 1 rows containing missing values (`geom_point()`).
## Warning: Removed 1103 rows containing missing values (`geom_line()`).

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Error in nls(fg_1, data = G_331, start = c(tau = tau.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_331, start = c(tau = tau.start, alpha = alpha.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    187     155.51                            
## 2    186     150.63  1 4.8775  6.0228 0.01504 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 631.7909
## 2     2 627.7361
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## tau     0.7899     1.6302   0.485  0.62858   
## alpha  -0.6637     0.2468  -2.689  0.00781 **
## A       3.8735     1.2352   3.136  0.00199 **
## k      59.6114    18.8470   3.163  0.00182 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8999 on 186 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.995e-06
##   (42 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    186     150.63                            
## 2    185     147.85  1 2.7851   3.485 0.06351 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 627.7361
## 2    2a 626.1902
## 3    2b 627.0534
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)   
## tau     0.81595    1.62271   0.503  0.61568   
## alpha   0.66637    0.23893   2.789  0.00584 **
## A       5.12725    2.17868   2.353  0.01965 * 
## k     147.54348  104.15313   1.417  0.15828   
## p       0.10195    0.03947   2.583  0.01057 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.894 on 185 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.375e-06
##   (42 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

predict and plot

## Warning: Removed 21 rows containing missing values (`geom_point()`).
## Warning: Removed 1120 rows containing missing values (`geom_line()`).

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    108     82.141                                
## 2    107     74.076  1 8.0648  11.649 0.0009079 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 317.2803
## 2     2 307.8092
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.9433     5.4470   0.357 0.721976    
## alpha  -0.9851     0.2476  -3.978 0.000127 ***
## A       3.2731     2.7047   1.210 0.228900    
## k      82.5474    33.3159   2.478 0.014786 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.832 on 107 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.997e-06
##   (13 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    107     74.076                           
## 2    106     74.076  1 0.000125  0.0002 0.9894
## 3    106     74.067  0 0.000000               
## 4    105     73.977  1 0.090103  0.1279 0.7213
##   model      AIC
## 1     2 307.8092
## 2    2a 309.8090
## 3    2b 309.7950
## 4    2c 311.6599
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     1.9433     5.4470   0.357 0.721976    
## alpha  -0.9851     0.2476  -3.978 0.000127 ***
## A       3.2731     2.7047   1.210 0.228900    
## k      82.5474    33.3159   2.478 0.014786 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.832 on 107 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.997e-06
##   (13 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

predict and plot

## Warning: Removed 4 rows containing missing values (`geom_point()`).
## Warning: Removed 1241 rows containing missing values (`geom_line()`).

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6431     5529.0                                
## 2   6430     5196.9  1  332.1  410.91 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24631.49
## 2     2 24234.93
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.81749    0.21414   3.818 0.000136 ***
## alpha -0.64323    0.02951 -21.793  < 2e-16 ***
## A      2.96500    0.11944  24.823  < 2e-16 ***
## k      1.87319    0.87956   2.130 0.033236 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.899 on 6430 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.313e-06
##   (344 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M211,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   6430     5196.9                              
## 2   6429     5190.8  1 6.1004  7.5556 0.005999 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 24234.93
## 2    2a       NA
## 3    2b 24229.38
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.80341    0.21262   3.779 0.000159 ***
## alpha  0.64462    0.02947  21.877  < 2e-16 ***
## A      2.92914    0.11295  25.933  < 2e-16 ***
## k     15.35544    3.85224   3.986 6.79e-05 ***
## s      4.27661    2.19938   1.944 0.051884 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8986 on 6429 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 6.485e-06
##   (344 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: fits
  • add s+p model: does not fit

predict and plot

## Warning: Removed 9 rows containing missing values (`geom_point()`).
## Warning: Removed 1108 rows containing missing values (`geom_line()`).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7778      13858                                
## 2   7777      13518  1 339.94  195.57 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 36650.46
## 2     2 36459.21
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.40077    0.18831   2.128   0.0333 *  
## alpha -0.81726    0.05533 -14.770  < 2e-16 ***
## A      4.31613    0.18952  22.774  < 2e-16 ***
## k     26.44060    3.72512   7.098 1.38e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.318 on 7777 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 9.35e-06
##   (405 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     2 36459.21
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    0.40077    0.18831   2.128   0.0333 *  
## alpha -0.81726    0.05533 -14.770  < 2e-16 ***
## A      4.31613    0.18952  22.774  < 2e-16 ***
## k     26.44060    3.72512   7.098 1.38e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.318 on 7777 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 9.35e-06
##   (405 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## Warning: Removed 27 rows containing missing values (`geom_point()`).
## Warning: Removed 982 rows containing missing values (`geom_line()`).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    843     1270.5                                
## 2    842     1225.9  1 44.684  30.692 4.045e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3539.637
## 2     2 3511.349
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     3.1536     1.6195   1.947   0.0518 .  
## alpha  -0.9337     0.1549  -6.029 2.47e-09 ***
## A       2.1122     0.4820   4.382 1.33e-05 ***
## k      26.3827    11.7080   2.253   0.0245 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.207 on 842 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.981e-06
##   (47 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223,  : 
##   singular gradient
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     2 3511.349
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     3.1536     1.6195   1.947   0.0518 .  
## alpha  -0.9337     0.1549  -6.029 2.47e-09 ***
## A       2.1122     0.4820   4.382 1.33e-05 ***
## k      26.3827    11.7080   2.253   0.0245 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.207 on 842 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.981e-06
##   (47 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## Warning: Removed 1 rows containing missing values (`geom_point()`).
## Warning: Removed 1175 rows containing missing values (`geom_line()`).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    952     1446.6                                
## 2    951     1370.3  1 76.287  52.943 7.178e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4071.286
## 2     2 4021.547
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     5.5388     2.8452   1.947  0.05186 .  
## alpha  -0.8352     0.1063  -7.857 1.06e-14 ***
## A       1.5900     0.4566   3.482  0.00052 ***
## k      13.1811     4.8742   2.704  0.00697 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.2 on 951 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 9.536e-06
##   (54 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     2 4021.547
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     5.5388     2.8452   1.947  0.05186 .  
## alpha  -0.8352     0.1063  -7.857 1.06e-14 ***
## A       1.5900     0.4566   3.482  0.00052 ***
## k      13.1811     4.8742   2.704  0.00697 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.2 on 951 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 9.536e-06
##   (54 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95392, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.8203, p-value = 1.434e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 8 rows containing missing values (`geom_point()`).
## Warning: Removed 1218 rows containing missing values (`geom_line()`).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3129     8568.5                                
## 2   3128     8205.0  1 363.57   138.6 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 16100.13
## 2     2 15966.34
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.65365    0.25317  -6.532 7.55e-11 ***
## alpha  -0.94510    0.07264 -13.010  < 2e-16 ***
## A      10.91594    0.93800  11.637  < 2e-16 ***
## k     104.82478    8.83904  11.859  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.62 on 3128 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.362e-06
##   (171 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3128     8205.0                                
## 2   3127     8163.5  1 41.421  15.866 6.954e-05 ***
## 3   3127     8181.8  0  0.000                      
## 4   3126     8126.6  1 55.197  21.232 4.231e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 15966.34
## 2    2a 15952.49
## 3    2b 15959.48
## 4    2c 15940.28
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -1.65297    0.25162  -6.569 5.90e-11 ***
## alpha   0.93030    0.07283  12.774  < 2e-16 ***
## A       9.21087    0.78875  11.678  < 2e-16 ***
## k     140.22607    9.54888  14.685  < 2e-16 ***
## p       0.32457    0.03009  10.786  < 2e-16 ***
## s       2.60360    0.44461   5.856 5.24e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.612 on 3126 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.473e-06
##   (171 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

predict and plot

## Warning: Removed 39 rows containing missing values (`geom_point()`).
## Warning: Removed 126 rows containing missing values (`geom_line()`).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1657     3824.4                                
## 2   1656     3744.5  1 79.903  35.337 3.375e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7969.307
## 2     2 7936.257
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.8503     0.3242  -5.707 1.36e-08 ***
## alpha  -0.7145     0.1114  -6.412 1.87e-10 ***
## A      13.9898     1.6309   8.578  < 2e-16 ***
## k     193.1434    23.7409   8.135 7.97e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.504 on 1656 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.696e-06
##   (333 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1   1656     3744.5                         
## 2   1655     3740.7  1 3.8563  1.7062 0.1917
## 3   1655     3740.8  0 0.0000               
## 4   1654     3740.6  1 0.1691  0.0748 0.7845
##   model      AIC
## 1     2 7936.257
## 2    2a 7936.547
## 3    2b 7936.589
## 4    2c 7938.514
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.8503     0.3242  -5.707 1.36e-08 ***
## alpha  -0.7145     0.1114  -6.412 1.87e-10 ***
## A      13.9898     1.6309   8.578  < 2e-16 ***
## k     193.1434    23.7409   8.135 7.97e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.504 on 1656 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.696e-06
##   (333 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

predict and plot

## Warning: Removed 149 rows containing missing values (`geom_point()`).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    347     171.17                                
## 2    346     151.29  1 19.881   45.47 6.515e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 858.0286
## 2     2 816.8144
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -2.2907     0.2919  -7.847 5.39e-14 ***
## alpha  -0.8298     0.1085  -7.647 2.06e-13 ***
## A      10.2668     1.9746   5.200 3.43e-07 ***
## k     170.6425    42.6923   3.997 7.84e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6612 on 346 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.574e-06
##   (17 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    346     151.29                          
## 2    345     150.77  1 0.51884  1.1872 0.2766
## 3    345     150.87  0 0.00000               
## 4    344     150.70  1 0.17087  0.3900 0.5327
##   model      AIC
## 1     2 816.8144
## 2    2a 817.6120
## 3    2b 817.8562
## 4    2c 819.4596
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -2.2907     0.2919  -7.847 5.39e-14 ***
## alpha  -0.8298     0.1085  -7.647 2.06e-13 ***
## A      10.2668     1.9746   5.200 3.43e-07 ***
## k     170.6425    42.6923   3.997 7.84e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6612 on 346 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.574e-06
##   (17 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

predict and plot

## Warning: Removed 1183 rows containing missing values (`geom_line()`).

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1671     1536.0                                
## 2   1670     1440.7  1 95.321  110.49 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4833.233
## 2     2 4727.986
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.71205    0.60194  -1.183    0.237    
## alpha -0.70634    0.05683 -12.429  < 2e-16 ***
## A      2.60054    0.41890   6.208 6.75e-10 ***
## k     45.32243    7.61770   5.950 3.27e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9288 on 1670 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.252e-06
##   (83 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M331,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M331,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1670     1440.7                                
## 2   1669     1425.2  1 15.487  18.136 2.171e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 4727.986
## 2    2a 4711.894
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.65228    0.61486  -1.061   0.2889    
## alpha   0.71340    0.05595  12.751   <2e-16 ***
## A       7.10119    4.82364   1.472   0.1412    
## k     638.51092  642.93098   0.993   0.3208    
## p       0.11674    0.06709   1.740   0.0821 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9241 on 1669 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.73e-06
##   (83 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## Warning: Removed 7 rows containing missing values (`geom_point()`).
## Warning: Removed 1091 rows containing missing values (`geom_line()`).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2489     2883.3                                
## 2   2488     2629.0  1 254.37  240.73 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8699.173
## 2     2 8471.019
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.83974    0.43909  -1.912   0.0559 .  
## alpha -0.90282    0.05006 -18.036  < 2e-16 ***
## A      4.58341    0.56859   8.061 1.16e-15 ***
## k     61.59170    6.83813   9.007  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.028 on 2488 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 9.108e-06
##   (129 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M332,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2488     2629.0                                
## 2   2487     2546.1  1 82.903   80.98 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 8471.019
## 2    2a 8393.170
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.88809    0.41840  -2.123 0.033885 *  
## alpha   0.88744    0.04965  17.873  < 2e-16 ***
## A      13.08533    4.76063   2.749 0.006027 ** 
## k     661.38696  325.80525   2.030 0.042462 *  
## p       0.08484    0.02516   3.371 0.000759 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.012 on 2487 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.975e-06
##   (129 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## Warning: Removed 53 rows containing missing values (`geom_point()`).
## Warning: Removed 1001 rows containing missing values (`geom_line()`).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1663     2105.7                                
## 2   1662     1836.5  1 269.18   243.6 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6652.568
## 2     2 6426.703
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau   -0.63995    0.55842  -1.146    0.252    
## alpha -0.94758    0.05301 -17.875  < 2e-16 ***
## A      5.64164    0.81725   6.903 7.21e-12 ***
## k     45.22933    5.02882   8.994  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.051 on 1662 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 8.953e-06
##   (92 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M333,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M333,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1662     1836.5                                
## 2   1661     1748.7  1 87.841  83.437 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 6426.703
## 2    2a 6347.049
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - 
##     alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.77897    0.50926  -1.530 0.126308    
## alpha   0.93774    0.05149  18.211  < 2e-16 ***
## A      16.98105    6.18278   2.747 0.006088 ** 
## k     704.86254  347.68787   2.027 0.042793 *  
## p       0.10435    0.03031   3.442 0.000591 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.026 on 1661 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.144e-06
##   (92 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## Warning: Removed 25 rows containing missing values (`geom_point()`).
## Warning: Removed 925 rows containing missing values (`geom_line()`).

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    343     334.98                                
## 2    342     308.64  1 26.333  29.179 1.238e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1054.269
## 2     2 1027.940
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.2716     1.0815  -0.251  0.80189    
## alpha  -0.8098     0.1322  -6.128 2.45e-09 ***
## A       2.6559     0.6651   3.993 7.98e-05 ***
## k      33.8809    10.6800   3.172  0.00165 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.95 on 342 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.796e-06
##   (105 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    342     308.64                           
## 2    341     308.47  1 0.173247  0.1915 0.6619
## 3    341     308.40  0 0.000000               
## 4    340     308.39  1 0.014347  0.0158 0.9000
##   model      AIC
## 1     2 1027.940
## 2    2a 1029.746
## 3    2b 1029.669
## 4    2c 1031.653
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + 
##     alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.2716     1.0815  -0.251  0.80189    
## alpha  -0.8098     0.1322  -6.128 2.45e-09 ***
## A       2.6559     0.6651   3.993 7.98e-05 ***
## k      33.8809    10.6800   3.172  0.00165 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.95 on 342 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.796e-06
##   (105 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

predict and plot

## Warning: Removed 42 rows containing missing values (`geom_point()`).
## Warning: Removed 1264 rows containing missing values (`geom_line()`).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 2a
212 Laurentian Mixed Forest 2b
221 Eastern Broadleaf Forest 2
222 Midwest Broadleaf Forest 2a
223 Central Interior Broadleaf Forest 2
231 Southeastern Mixed Forest 2
232 Outer Coastal Plain Mixed Forest 2c
234 Lower Mississippi Riverine Forest 2
242 Pacific Lowland Mixed Forest 2
251 Prairie Parkland (Temperate) 2
255 Prairie Parkland (Subtropical) 2
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert 2
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe 2a
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert 2
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2b
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2
M223 Ozark Broadleaf Forest Meadow 2
M231 Ouachita Mixed Forest 2
M242 Cascade Mixed Forest 2c
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 2
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 2a
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2a
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2a
M334 Black Hills Coniferous Forest 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 6884 2879 0.1883607 0.0290087 -0.1455213 0.5222427 0.6274918 0.0011929 0.5597848 0.6951988 3.795766 3.3198881 4.271643 70.361497 -45.538736 186.261731
212 Laurentian Mixed Forest east 22685 9493 1.3571172 0.0312721 1.0104959 1.7037384 0.8101887 0.0004854 0.7670035 0.8533738 3.136415 2.7436151 3.529215 19.515960 11.469758 27.562163
221 Eastern Broadleaf Forest east 7307 3560 -0.6755457 0.0172735 -0.9331864 -0.4179050 -0.7422922 0.0015343 -0.8190780 -0.6655063 5.357021 4.9706988 5.743343 23.626902 18.172427 29.081377
222 Midwest Broadleaf Forest east 5846 2589 0.0382426 0.0486224 -0.3940493 0.4705344 0.7592017 0.0020633 0.6701495 0.8482538 8.421344 5.5604167 11.282271 317.272977 100.111085 534.434868
223 Central Interior Broadleaf Forest east 10006 3860 -0.5940199 0.0148218 -0.8326695 -0.3553703 -0.6765477 0.0016337 -0.7557781 -0.5973173 5.146801 4.7832031 5.510400 42.046115 35.434811 48.657418
231 Southeastern Mixed Forest east 12844 5935 1.7191727 0.0370065 1.3420956 2.0962499 -0.8762149 0.0003803 -0.9144425 -0.8379874 3.818098 3.5992055 4.036990 2.559496 1.788330 3.330662
232 Outer Coastal Plain Mixed Forest east 13167 6463 1.3723711 0.0402169 0.9792790 1.7654632 0.8717178 0.0003915 0.8329322 0.9105035 3.891356 3.6002987 4.182414 26.061483 16.407657 35.715308
234 Lower Mississippi Riverine Forest east 1344 759 0.8095486 0.4801207 -0.5498176 2.1689147 -0.7606008 0.0060068 -0.9126498 -0.6085519 3.983594 2.9887786 4.978409 3.723276 1.028469 6.418082
242 Pacific Lowland Mixed Forest west 85 85 -0.9701074 2.9973158 -4.4189856 2.4787708 -0.9704833 0.1118949 -1.6368554 -0.3041112 9.751690 0.8264274 18.676952 20.975900 -9.935584 51.887383
251 Prairie Parkland (Temperate) east 2290 903 0.4135710 0.2070395 -0.4788649 1.3060069 -0.3868200 0.0121743 -0.6032275 -0.1704126 3.406591 2.8040034 4.009178 19.889791 12.653732 27.125849
255 Prairie Parkland (Subtropical) east 714 318 0.4255101 0.8895754 -1.4265887 2.2776089 -0.7802093 0.0193453 -1.0533335 -0.5070851 2.809477 1.8108544 3.808100 1.897828 -2.460867 6.256522
261 California Coastal Chaparral Forest and Shrub west 26 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest west 159 157 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert west 218 218 -1.3054454 0.8048950 -3.0744441 0.4635532 -0.8771256 0.0607386 -1.3630742 -0.3911770 5.101849 1.7119172 8.491781 144.962107 46.963721 242.960492
315 Southwest Plateau and Plains Dry Steppe and Shrub west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe west 331 255 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe west 232 128 0.8159476 2.6331754 -2.3854407 4.0173358 0.6663747 0.0570885 0.1949928 1.1377567 5.127250 0.8290002 9.425499 147.543476 -57.937096 353.024047
341 Intermountain Semi-Desert and Desert west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert west 124 123 1.9432557 29.6698155 -8.8547877 12.7412991 -0.9850791 0.0613271 -1.4760025 -0.4941556 3.273060 -2.0887741 8.634895 82.547372 16.502570 148.592174
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6778 3008 0.8034138 0.0452068 0.3866101 1.2202176 0.6446201 0.0008682 0.5868588 0.7023815 2.929143 2.7077264 3.150559 15.355443 7.803771 22.907115
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8186 3765 0.4007711 0.0354588 0.0316423 0.7698999 -0.8172623 0.0030615 -0.9257254 -0.7087992 4.316127 3.9446096 4.687644 26.440600 19.138368 33.742832
M223 Ozark Broadleaf Forest Meadow east 893 348 3.1536219 2.6226423 -0.0250255 6.3322692 -0.9337355 0.0239854 -1.2377165 -0.6297546 2.112200 1.1660418 3.058359 26.382711 3.402327 49.363095
M231 Ouachita Mixed Forest east 1009 496 5.5387856 8.0950993 -0.0447882 11.1223595 -0.8352323 0.0112997 -1.0438425 -0.6266222 1.589979 0.6939600 2.485998 13.181124 3.615640 22.746607
M242 Cascade Mixed Forest west 3303 3286 -1.6529736 0.0633113 -2.1463255 -1.1596216 0.9303037 0.0053036 0.7875131 1.0730943 9.210866 7.6643535 10.757379 140.226074 121.503360 158.948787
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow west 1993 1828 -1.8503008 0.1051331 -2.4862690 -1.2143326 -0.7144990 0.0124187 -0.9330755 -0.4959224 13.989840 10.7910407 17.188639 193.143382 146.578088 239.708676
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow west 367 367 -2.2907012 0.0852283 -2.8648995 -1.7165028 -0.8297544 0.0117744 -1.0431762 -0.6163326 10.266782 6.3831165 14.150447 170.642491 86.673365 254.611616
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow west 1757 1757 -0.6522770 0.3780549 -1.8582584 0.5537044 0.7133954 0.0031300 0.6036633 0.8231276 7.101191 -2.3598385 16.562221 638.510917 -622.525139 1899.546973
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow west 2621 2611 -0.8880933 0.1750560 -1.7085356 -0.0676510 0.8874392 0.0024653 0.7900755 0.9848030 13.085334 3.7501276 22.420540 661.386957 22.509468 1300.264447
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow west 1758 1747 -0.7789660 0.2593496 -1.7778326 0.2199007 0.9377412 0.0026516 0.8367420 1.0387404 16.981052 4.8541978 29.107907 704.862539 22.909901 1386.815177
M334 Black Hills Coniferous Forest west 451 179 -0.2715511 1.1695390 -2.3986862 1.8555841 -0.8098118 0.0174641 -1.0697448 -0.5498788 2.655893 1.3477070 3.964080 33.880890 12.874075 54.887704
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow west 220 220 NA NA NA NA NA NA NA NA NA NA NA NA NA NA

parameter variance co-variance

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation ideoms with `aes()`
## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 11 rows containing missing values (`geom_point()`).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 11 rows containing missing values (`geom_point()`).